Acoustic pulse propagation in forests

The propagation of acoustic pulses through a forest is considered. Multiple-scattering effects are accounted for by using the energy-based radiative transfer theory under a modified Born approximation, resulting in an expression for the diffuse intensity as a function of time and dominant frequency. While this expression is a complicated set of three integrals, certain practical approximations enable analytic evaluation of one, two, or even all three integrals. Any remaining integrals may be numerically calculated. The simple case of an impulse in an infinite homogeneous forest of diffuse scatterers is first considered, and then the effects of successively including non-diffuse scatterers, ground reflections in a forest of finite height, and finally a realistic forest model are analyzed with an emphasis on long-time decay and reverberation times. These theoretical findings are then compared with experimental results.